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In this paper we consider the Itô–Schrödinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the correlation length of the medium is smaller than the initial beam width. In terms of applications we prove that the centered fourth-order moments of the field satisfy the Gaussian summation rule, we derive the covariance function of the intensity of the transmitted beam, and the variance of the smoothed Wigner transform of the transmitted field. The second application is used to explicitly quantify the scintillation of the transmitted beam and the third application to quantify the statistical stability of the Wigner transform.  相似文献
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In this paper we extend previous work on time reversal in randomly layered media [J.-P. Fouque, J. Garnier, A. Nachbin, K. Sølna, Time reversal refocusing for point source in randomly layered media, Wave Motion 42 (2005) 238–260]. We consider first the case of an active source embedded below the surface in a finely layered random medium. We carry out time reversal with a time reversal mirror placed at the surface and we consider here the case where this mirror is larger than the carrier wavelength. In contrast with the situation addressed in our previous paper, where the size of the mirror was comparable to the wavelength, we show that multi-pathing dramatically enhances the effective aperture of the mirror so that super resolution at the location of the source can be obtained. In other words, the focal spot radius of the refocused field obtained in the case of a multiply scattering medium is much smaller than the spot size obtained in the case of a homogeneous medium. This super resolution effect is obtained by time-reversing the long incoherent waves generated by the multiple scattering due to the thin layers. We also give an application to the problem of focusing on a passive scatterer buried in the random medium and illuminated by a source at the surface.  相似文献
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